As an accountant in charge of reducing expenditures for a local company, you thi

Question

As an accountant in charge of reducing expenditures for a local company, you think you can save considerable money on fuel costs by lowering the room temperature of the building for daily use. In the morning, the interior temperature is typically 37.6 degree F and the thermostat is typically set for 72.4 degree F. Instead, you propose to lower the thermostat to 61.5 degree F. Currently the building measures 23.5 *44.7 * 14.5 feet. How much heat will be saved each morning by bringing the building up to the new operating temperature of 61 .5 degree F instead of 72.4 degree F Ignore heat and air losses to the outside and consider air an ideal diatomic gas. Assume that in the morning the pressure in the room is atmospheric. Express your answer as a positive quantity. The electricity rate in your area is $5.56 per kilowatt-hour. How much money (in dollars) is saved each morning by only heating the room to the new operating temperature* * This represents only a fraction of the cost savings, since higher interior temperatures induce higher losses of heat to the outside.

Explanation / Answer

V =23.5*44.7*14.5*0.3048^3 =431.308m^3

T= 37.6 oF=(37.6-32)/1.8 =3.11oC =276.11 oK

n= P*V/(R*T) =101325*431.308/(8.314*276.11 )=19037.59moles

Cv =5/2*R for diatomic gases

Q1=n*Cv*(T-To)=19037.59*5/2*8.314*(72.4-37.6)=13.77*10^6J

Q2= 19037.59*5/2*8.314*(61.5-37.6)=9.457*10^6J

Energy saved =Q1-Q2 =4.31*10^6J

kW hour = 60 x 60 = 3600*10^3 Joules

=>Energy saved =4.31*10^6/(3.6*10^6) kWh=1.1980kWh

money saved =$5.56*1.1980 =$6.66

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